Test 3 Section 3 #20

To get this one, first draw triangle ABC with the information given: angle B is a right angle,
BC = 16, and AC = 20.


Because you know your Pythagorean triples, you know that this is a big cousin of the 3-4-5 triangle—it’s a 12-16-20!


Now, let me point out something that you may already have realized: if triangle DEF is similar to triangle ABC, that means it has the same angles! Since the sine of an angle is always the same ratio regardless of the lengths of the sides in any particular triangle, we don’t need to draw DEF or calculate its side lengths to know what the sine of angle F is! The question tells us that angle F corresponds to angle C, so sin F = sin C. All we need to do is calculate the sine of C. So, SOH-CAH-TOA that bad boy.

\sin F=\sin C =\dfrac{12}{20}=\dfrac{3}{5}

Note that you can grid the fraction, 3/5, or the decimal equivalent .6 and be correct.

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